Let's roll this back a bit to where you had (or suspected) that you had a live connection.
If you can achieve that state again, run the local machine ping 127.0.0.1 on each PC just to make certain that the TCP/IP stack is running properly on the machines.
Next logical step is to try to ping each PC address from the other - you know how to do this so for the sake of brevity I'll skip the steps involved.
Next point to check, open Internet Explorer and check your connection parameters using Tools >> Internet options >> Connections.
Make sure there are no remaining references to dial up or other previous connections that may be a legacy from your old setup.
Finally, and I hate to suggest this since i'm sure you'll have done it already, triple check that all machines have a unique name, that they are all on EXACTLY the same workgroup, and check which type of network connection the Windows 98 machine is set to log in as.
The simplest solution would be to buy a wireless router/gateway that can natively support ALL machines.
Internet Connection Sharing is likely to be your enemy here, not the base networking setup. The two are linked but not the same thing at all and getting two wireless PCs to connect and share an internet connection are not necessarily the same thing at all.